Coach Ralph Hasenhüttl revealed the decision on Friday after the 24-year-old's impressive campaign last time out when he played a big role in helping Leipzig to the runners-up spot in the Bundesliga.
The centre-back was often the stand-in skipper last season as Kaiser only made seven league starts and he will now lead the team in the upcoming campaign.
"Willi Orban will be the new captain," Hasenhüttl said. "He always sets an example and is well-respected within the team."
Orban added: "I'm the kind of guy who is happy to take on responsibility. It's a real show of faith from the club, and I want to justify their decision.
"As captain, I want to lead the way with my performances and be a link between the team and the management."
Leipzig take on seventh-tier Sportfreunde Dorfmerkingen in the first round of the DFB Cup this weekend before beginning the new Bundesliga season at Schalke on August 19.